This has been bugging me a bit, if only because I know there is an answer to it.
So if you scour through the FF manuals, back of box text, and news posts for the game, the five wizards of the game do have names, but only one has ever been directly attached to the character.
The five players are the green male wizard, the yellow female wizard, the blue male wizard, the red female wizard, and the purple skull wizard. The names referenced in the bits of flavor text I've been able to dig up include Aliviana (attached to female pronoun), Callista (female), Talthas (male), and Dauziel (male).
Dauziel is without doubt the purple skull wizard since he's directly referred to in the Malefic Curses expansion, but everyone else gets real fuzzy:
Aliviana is said to wear slippers (" Aviliana’s slippers made no sound as she stalked her quarry down the stone corridor."), so she is most likely the yellow wizard, as the red wizard is barefoot. And if that logic holds true, the red wizard would then be Callista. Talthas doesn't give any clues to his identity, however, the green wizard is the one prominently shown on the box art, so if I had to take a guess, it would be him.
I acknowledge this is pretty shaky logic, and it still leaves us with no name for the blue wizard. If someone can offer some clarity, I'd really appreciate it! It's admittedly not an important aspect of the game, but I'd definitely like to know!